Generally, all diploid species pass through a haploid phase in their life. This is called the alternation of generations and the cycle may be presented like this:
Commonly we see organisms that spend most of their life in the diploid phase, with greatly reduced haploid phase (e.g. humans "live" in haploid state only as gametes). However, this is not the only way possible. There are organisms, which spend similar amount of time in each phase, which change ploidy depending on the conditions of the environment and, of course, organisms which spend most of their lives as haploids, with only a short diploid stage.
As a rule, lower plants, fungi and protozoa may exibit this behaviour. Some examples:
- Saccharomyces cerevisiae (yes, baker's yeast) will undergo meiosis and form haploid spores in unfavourable conditions, which then can grow as haploid colonies until they encounter a colony of opposite "sex"
- Mosses commonly grow larger gametophytes (haploid) than sporophytes (diploid)
- Some brown algae grow sporophytes and gametophytes that are indistinguishable form each other
- Ferns often grow large sporophytes and small, but self-sufficient gametophytes.
Next question should be "why only lower plants and fungi?" And the shortest answer is that a diploid organism is usually more robust, it can survive more potentially lethal mutations than a haploid.